18234
J. Phys. Chem. 1996, 100, 18234-18239
Study of Copper Sulfide Film Formation by Voltammetry Combined with Electrochemical Quartz Crystal Microgravimetry/Coulometry and Optical Spectroscopy Norma R. de Tacconi* and Krishnan Rajeshwar* Department of Chemistry and Biochemistry, The UniVersity of Texas at Arlington, Arlington, Texas 76019-0065
Reynaldo O. Lezna INIFTA, UniVersidad Nacional de La Plata Suc. 4, C.C. 16, La Plata (1900), Argentina ReceiVed: July 16, 1996; In Final Form: September 13, 1996X
This paper describes a study of copper sulfide film formation at copper anodes in sulfide-containing aqueous NaOH media. Voltammetry along with combined electrochemical quartz crystal microgravimetry (EQCM)/ coulometry showed the formation of an initial Cu2S (chalcocite) phase. Further oxidation resulted in a nonstoichiometric overlayer culminating in a surface that was CuS (covellite) in composition. The EQCM data also revealed incipient dissolution of the copper surface in the alkaline sulfide media as Cu(I) species. Chemical sulfidization of the copper surface is also shown to be an important film formation pathway. Complementary spectroscopic data were obtained in situ by visible reflectance spectroscopy and laser Raman spectroscopy. Ex situ analysis of the copper sulfide layer composition by X-ray photoelectron spectroscopy is also presented.
Introduction The Cu-S binary system consists of the stoichiometric end members Cu2S (chalcocite) and CuS (covellite), with a number of intermediate phases including Cu1.97S (djurleite), Cu1.8S (dijenite), Cu1.4S (anilite) and Cu1+xS (“blue-remaining” covellite).1 The optical and electrical properties of these materials have been the topic of many studies.2-6 In general, they are p-type semiconductors with copper vacancy defects as acceptors. Both direct and indirect band-to-band optical transitions have been observed for copper sulfides at wavelengths lower than 1250 nm.7 A shift in the absorption maximum to lower wavelengths with decreasing copper content has been attributed to a progressively lower Fermi level with the Fermi levelconduction band edge gap increasing from Cu2S to CuS.7 Much of the interest in the optical properties of copper sulfides stems undoubtedly from their use in CuxS/CdS solar cells. However, copper sulfides are also important in potentiometric sensor devices, and are potentially of interest in electrochromic applications. Studies oriented toward the electrochemical growth of CuxS are relatively scarce. Galvanostatic deposition on a copper anode from an acidic solution saturated with H2S was shown to afford copper sulfide layers of decreasing copper activity as the oxidation proceeded.8 Potentiostatic current transients from copper electrodes in NaOH solutions of varying Na2S content were analyzed to reveal a complex sequence of copper sulfide film formation, subsequent rupture of this film, and copper oxide formation.9 CuxS films with x ranging from 1 to nearly 2 were deposited at temperatures from 21 to 120 °C from a propylene glycol bath containing CuNa2EDTA (EDTA ) ethylenediaminetetraacetic acid), elemental sulfur, and KCl.10 High deposition temperatures (e.g., 80 °C) and low current densities (∼10-4 A cm-2) were reported to yield relatively large twinned crystals of Cu2S by the anodic oxidation of copper in sulfidecontaining aqueous electrolytes.11 We describe in what follows a systematic in situ study of * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)02125-9 CCC: $12.00
anodic CuxS film growth by voltammetry combined with electrochemical quartz crystal microgravimetry/coulometry. These measurements were complemented by in situ visible reflectance and laser Raman spectroscopies and ex situ analyses of the CuxS layers by X-ray photoelectron spectroscopy. We show that both chemical and electrochemical reactions contribute to film growth, and that incipient CuxS film formation is initiated by Cu dissolution as a monovalent species. We additionally show that CuxS film growth can be studied with no interference from oxide formation (cf. ref 9) by carefully restricting the range of potentials to values negative of ca. -0.5 V (vs Ag/AgCl reference). Experimental Section The working electrodes for voltammetry in this study were 5.0 mm diameter copper rods (Johnson Matthey, 99.999%) encased in a Kel-F shroud. Their surfaces were polished to a mirror finish with Al2O3 (Buehler) down to 0.05 µm followed by ultrasonication in distilled water. A conventional singlecompartment three-electrode electrochemical cell was used with a Pt spiral as the counter electrode and a Ag/AgCl/3 M KCl electrode as reference. All potentials in this work are quoted with respect to this reference. The films were grown in dilute sulfide solutions (nominal pH 13) of composition y mM Na2S (with 0.1 mM > y > 10 mM) + 0.1 M NaOH. The NaOH solutions were thoroughly deoxygenated (with ultrapure N2 gas purge) prior to Na2S addition to preclude the formation of polysulfide species. The copper electrode was polarized at -1.4 V prior to CuxS film growth to reduce any residual oxide layer. Electrochemical measurements (voltammetry, coulometry) and potential control for film growth utilized an EG&G Princeton Applied Research Model 273 instrument. The setup for electrochemical quartz crystal microgravimetry (EQCM) has been previously described.12 A 5 MHz AT-cut quartz crystal (Valpey-Fisher) with copper deposited on either side was used for the EQCM measurements. The area exposed to the electrolyte was 0.79 cm2. Reflectance measurements were obtained with a computerized optical multichannel analyzer fitted with a cooled Si diode array © 1996 American Chemical Society
Copper Sulfide Film Formation
J. Phys. Chem., Vol. 100, No. 46, 1996 18235
Figure 2. Cyclic voltammograms (potential scan rate 25 mV/s) of a polycrystalline copper electrode in a 0.1 M NaOH solution containing (a) 0.5 mM Na2S and (b) 5 mM Na2S. Scan details as in Figure 1; see the text for description of the various labeled peaks.
Figure 1. Cyclic voltammograms (potential scan rate 50 mV/s) of a polycrystalline copper electrode in (a) 0.1 M NaOH and (b) 0.1 M NaOH + 2 mM Na2S. The scans were initiated at -1.4 V and in the positive direction. In part a, the electrode was held at -1.4 V for 1 min between cycles.
capable of detecting changes of 10-5 in ∆R/R with a time resolution of ca. 200 ms. This rapid-scan spectrometer was employed to obtain integral spectra as a function of time during the film growth. Nonpolarized light at an incident angle of 59° was used. Each spectrum consisted of 50 exposures with each exposure averaging 0.03 s on the diode array chip. This translates to a total acquisition time of ca. 1.5 s for each spectrum. The blank spectrum (R0) was obtained first at -1.4 V (bare copper surface); then a potential step was applied and successive spectra were acquired during the film growth. Consecutive spectra (Rf) were obtained with an elapsed time of 30 s between spectra. Spectra were plotted as (Rf - R0)/R0 vs wavelength, in the range 300-900 nm. Laser Raman spectroscopy employed the 514.5 nm line of an Ar+ ion laser operated in conjunction with a Spex Ramalog instrument; further details are given elsewhere.13-15 X-ray photoelectron spectroscopy (XPS) was performed on a Physical Electronics Model 5000C system fitted with an aluminum anode (1486.6 eV). The analyzer had a pass energy of 17.90 eV with a resolution of 0.60 eV for Ag (3d5/2) standard. All chemicals were from comercial sources and were of the highest purity available. They were used as received. All solutions were made from Corning Megapure water. All the experiments below pertain to the laboratory ambient temperature. Results and Discussion Voltammetry. The cyclic voltammograms in Figure 1 underline the importance of using a restricted potential domain for CuxS film growth such that copper oxide/hydroxide forma-
tion is avoided. The voltammograms in Figure 1a were obtained for a copper rod in 0.1 M NaOH. The various oxide/hydroxide phases on the copper anode surface on the forward scan are identified along with the reduction peaks on the return cycle. On the other hand, when the NaOH solution is dosed with Na2S (2 × 10-3 M in this case), a new set of peaks (labeled A1 and C1) appears as shown in Figure 1b. These correspond to the growth and subsequent reduction of CuxS respectively on the copper surface. For all subsequent experiments, the positive limit of the potential excursions was always kept below -0.5 V to preclude the complications from oxide/hydroxide phase formation. This contrasts with an earlier study9 wherein the effect of copper sulfide on subsequent corrosion and pitting of the copper surface was investigated. Figure 2 contains cyclic voltammograms illustrating the effect of varying Na2S concentration on the CuxS film formation/ reduction profiles. Thus, Figure 2a and 2b correspond to 0.5 and 5 mM Na2S in the 0.1 M NaOH electrolyte. In addition to the peaks labeled A1 and C1 (cf. Figure 1), two other features appear in Figure 2: A0 and C2. The weak anodic wave A0 is located negative of the open circuit potential, ca. -0.95 V. This is assigned to the underpotential deposition (UPD) of a hydrosulfide layer on the copper surface according to the following sequence of steps:
xCu + HS- f Cux(HS)ads-
(1)
Cux(HS)ads- f Cux(HS)ads + e-
(2)
A similar behavior pattern occurs at the Au surface.16 This reaction sequence obviously depends on the sulfide concentration in solution, and is manifested as the marked sensitivity of the A0 wave amplitude to this variable (cf. Figure 2a and 2b). The involvement of HS- (rather than S2-) in reactions 1 and 2 arises from the fact that the hydrolysis equilibrium
S2- + H2O a HS- + OHlies far to the right.
(3)
18236 J. Phys. Chem., Vol. 100, No. 46, 1996
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The formation of copper sulfide films predominantly occurs over the range of potentials corresponding to the main anodic peak, A1, according to the following global reaction:
Cux(HS)ads- f CuxS + 2e- + H+ (1 e x e 2)
(4)
For dilute sulfide solutions (e1.0 mM) such as the ones mostly employed in this study, this reaction yields smooth, shiny films on the copper surface. These films are of a purple hue up to an anodic charge of 4-5 mC/cm2. Subsequent film growth changes its coloration to a bluish yellow hue. Reaction 5 would account for these observations:
CuxS + yHS- f Cux-yS + yCuS + yH+ + 2ye-
(5)
The Cux-yS nonstoichiometric phases (containing different amounts of Cu+ and Cu2+ species) thus account for the gradual change in the electrode surface appearance. The electrochromic changes are quite reversible as long as the positive potential limit does not exceed -0.55 V. Further, the electrochromism can also be provoked by potential steps (instead of sweeps). However, prolonged switching or cycling (>50 cycles) instigates darkening of the electrode surface. At higher sulfide concentrations (e.g., 5 mM, Figure 2b), the copper electrode darkens in the first potential cycle itself and remains black during subsequent cycles. The voltammograms in this case manifest two cathodic peaks that grow somewhat in amplitude during prolonged cycling. In both cases in Figure 2, the cathodic cycle encompasses a distinctly higher charge (Qc) than its anodic counterpart (Qa). This is clear evidence for the existence of a chemical film formation pathway that occurs in parallel with the electrochemical film growth step. To study this further, a copper electrode was introduced in the sulfide solution after being initially poised at -1.3 V to assure a pristine surface free of oxide/sulfide (see the Experimental Section). Then the electrode was disconnected and allowed to evolve to its rest point (Eτ ) -0.95 V) where it was held for preselected times (τ) prior to initiating a cathodic (negative-going) scan. Figure 3a contains the results. Note that only one cathodic peak is present. In contrast, reduction of a film formed at Eτ ) -0.85 V (i.e., positive of the open-circuit value) for varying periods of time (τ) yields a composite cathodic wave profile (Figure 3b) reminiscent of the pattern seen earlier in Figure 2b. Interestingly, a single peak is seen here also in the early stages (τ ) 2 min) of film growth, and this peak corresponds roughly in location to that seen in Figure 3a (the peak labeled C1 earlier in Figure 2b). At longer τ, the single peak becomes broader with an increasing contribution of a shoulder on its negative side. The voltammetry data in Figures 2 and 3 are consistent with the formation of distinct inner and outer layers on the copper surface. Further, both UPD (reactions 1 and 2) and chemical reactions (i.e., sulfidization) contribute to film growth at potentials negative of the open-circuit value. The latter is favored by the very low solubility product (Ksp) of Cu2S (Ksp ) 3.0 × 10-49, ref 17):
2Cu + HS- f Cu2S + H+ + 2e-
(6)
The voltammetric evidence for a two-layer growth is consistent with the model developed by a previous author.8 This previous study concluded that the first layer was comprised of Cu2S, and that further layer growth was controlled by the ratio of Cu2+ and Cu+ in the new phase. Accordingly, we assign the peak C1 to the Cu2S (chalcocite) phase, and C2 to the
Figure 3. Cathodic voltammograms of a polycrystalline Cu electrode in 0.5 mM Na2S + 0.1 M NaOH after being held at Eτ for different times (τ). (a) Eτ ) -0.95 V (open circuit) and τ ) 2, 3, 6, 12, and 20 min (top to bottom); (b) Eτ ) -0.85 V and τ ) 2, 3, 6, and 12 min. (top to bottom). The potential scan rate was 20 mV/s. After each scan, the electrode was cleaned, repolished, and introduced in the sulfide solution at -1.4 V to start with a memory-free surface.
nonstoichiometric copper sulfide formed atop this initial Cu2S layer (reaction 5). Further compositional details on these layers are furnished by the spectroscopic data to be discussed later. Electrochemical Quartz Crystal Microgravimetry/Coulometry and ex Situ XPS. For the combined EQCM/coulometry measurements, the Cu films (on the quartz wafer) were initially poised at -1.4 V as before. The potential was then stepped (or swept at 1 V/s) to selected values in the range from -0.93 to -0.85 V. Both the frequency change (∆f) and the anodic charge (Qa) were monitored at times up to 20 min. Longer times were avoided as the initial smooth films became rough and black with progressive oxidation (see above). Figure 4 contains EQCM/coulometry data for a potential step from -1.4 to -0.85 V. Qa shows a steady increase following a parabolic law (not shown) as expected for a film growth process controlled by diffusion of copper ions through the growing film.8 Concomitantly, ∆f showed an initial increase followed by a monotonic decrease brought about by growth of the copper sulfide layer. The initial frequency increase is better manifested when a subsequent potential step was applied after the film electroreduction (Figure 4, insert). This initial frequency increase (mass loss) is assigned to the reaction:
Cux(HS)ads- f xCu+ + HS- + xe-
(7)
Clearly, voltammetry data alone would not have revealed this incipient electrodissolution reaction, and this underlines the advantage gained by adding the EQCM probe18,19 to the electrochemical measurements.
Copper Sulfide Film Formation
J. Phys. Chem., Vol. 100, No. 46, 1996 18237
Figure 4. Combined frequency/time and anodic charge/time profiles obtained during copper sulfide film growth at -0.85 V in 0.5 mM Na2S + 0.1 M NaOH on a freshly polished copper electrode. The inset shows a second run at the same potential obtained after electroreduction.
Figure 5. Plot of anodic charge vs mass change at -0.85 V at times less than 1 min in the combined EQCM/coulometry experiment.
Figure 6. Time evolution of Qa and Qc for a copper sulfide film grown at -0.85 V in 0.5 mM Na2S + 0.1 M NaOH. The anodic charge was recorded during potentiostatic film growth at -0.85 V. The cathodic charge was obtained potentiodynamically at 20 mV/s after film growth for each preselected time interval at -0.85 V (see inset).
Figure 7. Plot of Qc vs mass change at -0.85 V for time intervals from 1 to 16 min. Refer to text for the origin of these data.
Reaction 7 is promoted by a less-ordered copper layer such as that formed by the electroreduction of a previously formed copper sulfide layer (cf. Figure 4, insert). It is worthy of note that the ∆f vs time profiles are less featured than the first one obtained for a pristine copper surface. The anodic charge, Qa, that is measured is partitioned into the electrodissolution reaction (eq 7) and the film formation reactions (reactions 4 and 5) as given by Faraday’s law:
Qa ) (F/MCu)(mCu+ + 2mCu2+) + (xF/MCuxS)mCuxS with 1 e x e 2 (8) In eq 8, F is the Faraday constant (96 485 C/mol), MCu and MCuxS are the molar masses of copper and copper sulfide respectively, mCu+ and mCu2+ are the masses involved in the dissolution of the copper sulfide layer in the +1 and +2 state, respectively, mCuxS is the mass of the copper sulfide layer deposited, and x is the electron stoichiometry in the CuxS phase. The measured frequency (∆f) is related to the mass change (∆m) by the Sauerbrey equation.20 The total mass change (∆m) is given by
Figure 8. Time dependence of the integral reflectance spectra obtained during the growth of a copper sulfide film on a Cu electrode in 0.5 mM Na2S + 0.1 M NaOH at -0.85 V. Spectra were acquired in 30 s time intervals increasing in time from bottom to top.
∆m ) ∆mCuxS - ∆mCu ) ∆mS - ∆mCu
(9)
In eq 9, we have further considered the increase in mass due to film growth (∆mCuxS) to be equal to the mass of sulfide entering the film (∆mS). This is because the film grows by the incorporation of HS- at the film/electrolyte interface.8 The
18238 J. Phys. Chem., Vol. 100, No. 46, 1996
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Figure 9. (A) Laser Raman spectrum obtained in situ for a copper sulfide film grown for 30 min at -0.85 V (Qa ) 28 mC/cm2) (spectrum a) in 0.5 mM Na2S + 0.1 M NaOH. Spectra b and c were obtained ex situ for authentic samples of CuS and Cu2S, respectively. (B) In situ laser Raman spectra for a fresh copper sulfide layer formed at -0.80 V (spectrum a). Spectra b and c correspond to progressive oxidation of the copper sulfide film at -0.2 V for 1 min and ca. 5 min, respectively.
TABLE 1: Ex Situ Analyses of the Copper Sulfide Layers Grown at -0.85 V by X-ray Photoelectron Spectroscopy growth time
element
peak area (cts-eV/s)
sensitivity
atomic concn (%)
2 min
S2p Cu2p S2p Cu2p
3 578 91 007 4 833 58 232
0.463 5.680 0.463 5.680
32.54 67.46 50.45 49.55
13 min
amount of copper involved in film formation originates from the electrode itself, and thus does not contribute to a mass change except through the dissolution reaction. Figure 5 shows a plot of Qa versus the initial mass decrease, ∆mCu, for times shorter than 1 min. From the slope of this plot, and using eq 10,
n)
( )
∆Qa MCu ∆m F
with (MCu/F) ) 6.58 × 10-4 g/C
(10)
a value of n ) 1.0 ( 0.2 was obtained. This value is consistent with the initial Cu dissolution step embodied in reaction 7 above. Figure 6 contains the composite Q vs t profiles both for Qa recorded at +0.85 V, and for the corresponding electroreduction charge, Qc, obtained from a negative-going scan at 20 mV/s following anodic steps for times ranging from 0.15 to 15 min (see Figure 6, inset). As mentioned earlier, Qc > Qa and Qc reflects the film formed by both electrochemical and chemical routes. Thus, the counterpart of eq 8 for Qc becomes
Qc ) [(xF/MCuxS)mCuxS]electrochem + [(xF/MCuxS)mCuxS]chem with 1 e x e 2 (11) where [(xF/MCuxS)mCuxS]electrochem involves the charge related to the mass changes brought about by electrochemical film growth and [(xF/MCuxS)mCuxS]chem is a similar term for the spontaneous chemical sulfidization reaction. Since Qc is better reflective of film growth (rather than Qa), this parameter may be used in conjunction with the measured mass change in a manner analogous to the plot in Figure 5. Such a plot is shown in Figure 7. The mass increase data were culled from Figure 4 and Qc values from Figure 6: both sets of
values were obtained under the same conditions and for times ranging from 1 to 16 min. Three broad regimes of film growth can be discerned in the plot in Figure 7, from which the electron stoichiometry can be estimated from the slopes:
n)
( )
∆Qc MS ∆m F
with (MS/F) ) 3.32 × 10-4 g/C (12)
The first and third regions in Figure 7 afford a value for n = 2, and the intermediate region features a lower n value. The first region comprises charges up to ca. 7 mC/cm2. Only one cathodic peak is observed for film electroreduction (Figure 3), pointing toward a film composition that is homogeneous in depth at this stage of growth. Correspondingly, a film synthesized with Qa = 5 mC/cm2 analyzes as Cu2S by XPS (Table 1). Thus, Cu/S = 2 and the charge/mass ratio manifests in Figure 7 as the uptake of one HS- anion per two Cu atoms that are oxidized to the Cu(I) state. The intermediate region in Figure 7 corresponds to charges between 7 and 12 mC/cm2. The film is still thin at this stage; however, unlike in the first region the chemical film growth pathway becomes competitive with the electrochemical route. Electroreduction of such a film yields the voltammetric profile shown in Figure 3b. The third film growth region in Figure 7 has an n value of =2 corresponding to the incorporation of one HS- anion per one Cu atom that is oxidized to the Cu(II) state. The outer part of the film thus has a stoichiometry of CuS. Correspondingly, a film grown with Qa = 14 mC/cm2 analyzes with a Cu/S ratio of near unity by XPS (Table 1). In summation of this section, the EQCM/coulometry and XPS data thus corroborate the voltammetry evidence for a two-layer film growth model8 with an inner layer comprising Cu2S (chalcocite) and an outer layer approaching the CuS (covellite) phase in composition. An intermediate transition zone features a graded composition of decreasing copper content outward. Reflectance Spectroscopy/Laser Raman Spectroscopy. Figure 8 shows the time dependence of the integral change of reflectance ∆R/R vs wavelength. Spectra were taken at 30 s
Copper Sulfide Film Formation intervals after a potential step from -1.4 to -0.85 V had been applied. The reflectivity of the surface was found to decrease as the anodic charge increases. The ∆R/R spectra recorded during film growth up to anodic charges of ca. 8 mC/cm2 showed an increasing broad absorption band composed mainly of two contributions: a broad maximum in the 530-600 nm domain that progressively shifts to the red, and another band at 620 nm that becomes the dominant one as the film grows. The latter coincides with the reported direct band transition for Cu2S.2-6 An increase of absorption toward the red as the film gets thicker was also observed, and is likely related to the indirect energy band gap of the film. Hence, the film possesses the characteristic color of the chalcocite phase and the reflectance changes are mainly associated with a thickness increase while the same composition is maintained. No electroreflectance effect contributions from the Cu substrate are expected to be present in these spectral changes because the reflectance changes were obtained at constant potential. At charges higher than 8 mC/cm2, the reflectance changes contain contributions from light interference effects from the outer CuS layer. Finally, at anodic charges higher than 15 mC/ cm2, the film tarnishes and becomes black. A series of discrete copper sulfide phases were identified by in situ reflectance spectroscopy7 during the anodic oxidation of chalcocite electrodes. The wavelength of absorbance maximum was found to shift from 2300-1200 nm to ca. 600 nm as the electrode progressively went through the djurleite, dijenite, “blue-remaining” covellite phases culminating in the CuS (covellite) phase.7 However, these spectra did not show features related to direct interband transitions at the early stages of film oxidation (i.e., CuxS with x = 2). In our limited wavelength range (Figure 8), the complex broad band in the 530-620 nm range is in agreement with the reported direct transitions observed in very thin films.2-6 The thicker films (Qa > ca. 15 mC/cm2) were characterized by laser Raman spectroscopy. Thus, a Raman band was detected at 470 cm-1 in situ during film growth at Qa = 28 mC/cm2 (Figure 9A, spectrum a). This band coincides with an analogous band observed for an authentic sample of CuS (Figure 9A, spectrum b). It must be noted that authentic samples of Cu2S do not exhibit any bands in the 300-800 cm-1 spectral range (Figure 9A, spectrum c). Correspondingly, the in situ Raman spectra were featureless in the early stages of copper sulfide film growth. Figure 9B contains a sequence of Raman spectra for a film initially formed at -0.80 V (spectrum a), and then progressively oxidized at -0.2 V for periods ranging from 1 min (spectrum b) to ca. 5 min (spectrum c). The 470 cm-1 Raman signature
J. Phys. Chem., Vol. 100, No. 46, 1996 18239 diminishes in intensity as the outer part of the CuS layer is converted to oxide (cf. Figure 1). Conclusions The evidence from voltammetry for an anodic copper sulfide layer growth model that is compositionally heterogeneous in depth has been verified by EQCM/coulometry and in situ spectroscopy measurements. Additionally, the EQCM probe has shown the presence of an initial film electrodissolution step involving the oxidation of Cu to the Cu(I) state. Chemical sulfidization of the copper has also been shown to be an important film growth pathway. Finally, in situ visible reflectance spectroscopy and laser Raman spectroscopy are shown to be complementary in that the former is effective at the early stages of copper sulfide film growth, whereas the latter has shed compositional light on the thicker films considered in this study. Acknowledgment. This study was funded in part by a grant from the Office of Basic Energy Sciences, U.S. Department of Energy. References and Notes (1) Ribbe, P., Ed. ReV. Mineral. 1982, 1, CS-58-CS-75. (2) Stanley, A. G. Appl. Solid State 1975, 5, 251. (3) Marshall, R.; Mitra, S. S. J. Appl. Phys. 1965, 36, 3882. (4) Mulder, B. J. Phys. Stat. Sol. A 1972, 13, 569. (5) Mulder, B. J. Phys. Stat. Sol. A 1973, 18, 633. (6) Mulder, B. J. Phys. Stat. Sol. A 1972, 13, 79. (7) Koch, D. F. A.; McIntyre, R. J. J. Electroanal. Chem. 1976, 71, 285. (8) Etienne, A, J. Electrochem. Soc. 1970, 117, 870. (9) Vasquez Moll, D.; De Chialvo, M. R. G.; Salvarezza, R. C.; Arvia, A. J. Electrochim. Acta 1985, 30, 1011. (10) Engelken, R. D.; McCloud, H. E. J. Electrochem. Soc. 1985, 132, 567. (11) Becker-Roes, D.; Fisher, A.; Schimmel, M.; Wendt, H. In Electrochemical Engineering and Energy; Lapicque, F., Ed.; Plenum, New York, 1995; p 73. (12) Bose, C. S. C.; Rajeshwar K. J. Electroanal. Chem. 1992, 333, 235. (13) de Tacconi, N. R.; Son, Y.; Rajeshwar, K. J. Phys. Chem. 1993, 97, 1042. (14) de Tacconi, N. R.; Rajeshwar, K. J. Phys. Chem. 1993, 97, 6504. (15) de Tacconi, N. R.; Lezna, R. O.; Rajeshwar, K. J. Phys. Chem. 1994, 98, 4104. (16) Lezna, R. O.; de Tacconi, N. R.; Arvia, A. J. J. Electroanal. Chem. 1990, 283, 319. (17) For example: Harris, D. C. QuantitatiVe Analysis, 3rd ed.; W. H. Freeman & Co.: San Francisco, 1991. (18) Mori, E.; Baker, C. K.; Reynolds, J. R.; Rajeshwar, K. J. Electroanal. Chem. 1988, 252, 441. (19) Wei, C.; Rajeshwar, K. J. Electroanal. Chem. 1994, 375, 109. (20) Sauerbrey, G. Z. Phys. 1959, 155, 20.
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